Several of the nation’s largest health insurance companies will stop issuing certain children’s insurance policies to avoid complying with a new mandate in the Democrats’ health care overhaul.

The insurers will no longer write “child-only” policies — a small, niche market — over concern that the health reform law will make the market unstable and unprofitable.

Beginning Thursday, insurance companies will no longer be allowed to turn down any child who applies for coverage, even if he or she has a pre-existing condition. It’s a benefit of health care reform that President Barack Obama and other Democrats tout frequently.

But insurers are worried that children — or, more likely, their parents — might apply for coverage literally on the way to the hospital or doctor’s office and cancel it once treatment is complete. The lack of child-only coverage has the potential to keep healthy consumers out of the market, driving up costs.

The scenario underscores the delicate relationship between the government mandates and the insurance marketplace that will be required for successful implementation of the health care reform law. It has also raised concerns about what will happen in 2014, when insurers won’t be able to turn down coverage for adults, either.

The Obama administration tried to address the issue over the summer, when insurers began notifying states that they would leave the market. The Department of Health and Human Services said companies would be able to establish “open enrollment periods” of about a month or so, in which customers could sign up for coverage, and close coverage the rest of the year.

The administration’s open-enrollment periods were designed to ensure that everyone has access to coverage without saddling insurers with unpredictable costs. But insurers say it’s not enough to make sure that healthy customers stay in the market. And it doesn’t address how to cover anyone — healthy or sick — outside the open enrollment period if, say, a child’s parent loses his or her job and coverage.

Anthem announced Friday that it will no longer write child-only policies after Thursday, citing the “unlevel competitive environment” created by the law. Aetna plans to leave the market in 26 states and the District of Columbia as of Oct. 1 and several other states later this fall. Cigna, Humana and several Blue Cross Blue Shield companies have already stopped writing the policies.

“We would love to stay in the market,” said G. William Hoagland, vice president of public policy at Cigna. But “you can’t have guaranteed issue for this population and be the only one out there. You can’t make it work financially.”

Child-only policies make up less than 10 percent of single-coverage plans sold directly to individuals, according to rough industry estimates. The changes won’t alter policies already in existence or coverage for kids on family plans.

Just days before the provision is due to go into effect, no one seems to have a clear solution in mind.

“It’s certainly one that we still haven’t gotten a handle on. It’s still out there, and its implementation date is rapidly approaching,” said Kansas Insurance Commissioner Sandy Praeger, who heads the health reform work at the National Association of Insurance Commissioners, which is advising HHS on the health law.

“This is one of those issues, had there been a [House-Senate] conference committee, it probably would have been worked out,” Praeger said.

HHS is still working with insurance companies on the issue and will offer additional regulatory guidance if necessary.

“Insurance companies have pledged to offer coverage to children with pre-existing conditions, and we expect them to honor that commitment,” said HHS spokeswoman Jessica Santillo. “Insurers shouldn’t break their promise and turn their backs on some of our most vulnerable Americans. The administration has emphasized from the start that it would work with states, employers, consumer advocates and insurers to maintain a balance between access to coverage for children with pre-existing conditions and choice of policies for all children.”

Insurers say they want to continue writing the policies but defend the move to leave the market.

“There remains a great deal of uncertainty as to how the rules will be implemented and what the impacts might be on participating insurers,” said Kristin Binns, a spokeswoman for Anthem.

Insurers say the only way to balance the government’s mandate that they not turn down any customers is by requiring that all Americans buy coverage, which would spread the risk. That requirement will go into effect in 2014, though some insurers say the penalties for not getting coverage may not be enough to persuade people to purchase it.

“The difficulty has been, if you have a policy that requires that all people participate, without having everyone in, you get those who perceive they will need insurance coverage [only] for an expensive condition,” said Karen Ignagni, president of America’s Health Insurance Plans.